Chiral Wess-Zumino model and breaking of supersymmetry

TL;DR

This paper demonstrates that the chiral Wess-Zumino model undergoes supersymmetry breaking at low energies through a mechanism similar to chiral symmetry breaking in QCD, involving instantons and a critical coupling.

Contribution

It establishes a connection between supersymmetry breaking in the Wess-Zumino model and chiral symmetry breaking in QCD, providing a new perspective on low-energy supersymmetry dynamics.

Findings

Supersymmetry is broken in the low-energy limit of the Wess-Zumino model.

The breaking mechanism parallels chiral symmetry breaking in QCD.

Instanton effects are crucial in the low-energy behavior of the theory.

Abstract

We prove that the Wess-Zumino model breaks supersymmetry in the low-energy limit. The mechanism is identical to the breaking of chiral symmetry in quantum chromodynamics as the low-energy limit is a Nambu-Jona-Lasinio model and the gap equation has a solution. This happens at a critical coupling at lower momenta. Instanton liquid plays an essential role in the behavior of the theory in this limit.